How to Calculate Wave Speed: Step-by-Step Guide for Students
First, we will understand the definition of a wave then we will move to wave speed. A wave is a disturbance that moves through a medium from one end to another end. It can be seen in the ocean water as an ocean wave moving along the medium. When we observe it carefully we can see that the crest of the wave is moving from one location to another over a given interval of time. This crest is observed to cover the distance. As we know that the speed of an object refers to how fast that object is moving and is usually expressed as the distance travelled per unit time of travel. We can also observe a wave when a source vibrates and disturbs a particle in the medium. It can usually be seen in the tuning fork or ripples in water when a body is dropped, etc. In this topic, we will discuss what wave speed is the formula with few solved examples.
What is Wave Speed?
Wave speed is defined as the speed at which a wave travels. It is related to wavelength, frequency and period. It is given by the formula v=fλ
Where v is the velocity of the wave,
f is the frequency of the wave, and
λ is the wavelength.
Wavelength is defined as the distance between two successive crests or troughs of a wave.
Wave frequency is the number of waves that pass through a fixed point in a given amount of time. The most commonly used wave speed is the speed of visible light and an electromagnetic wave.
The Speed of a Wave
The speed of a wave is defined as the distance a wave travels in a given amount of time. It is the number of meters it travels per second. Wave speed can be represented by the equation:
\[Speed=\frac{Distance}{Time}\]
Properties of Waves
Following are the properties of waves:
Amplitude – Amplitude is the maximum height of the wave, usually measured in meters.
Wavelength – It is the distance between identical points in the adjacent cycles of crests as well as the trough of a wave. It is also measured in meters.
Period – It is defined as the time taken by a particle on a medium to make one complete vibrational cycle. It is measured in units of time such as seconds or minutes.
Frequency – The frequency of a wave is defined as the number of waves passing a point in a certain time. The S.I unit of frequency is hertz (Hz) which is equal to one wave per second.
The period can also be defined as the reciprocal of the frequency and vice versa.
\[Period=\frac{1}{Frequency}\]
Speed – The speed of a wave refers to the distance travelled by a given point on the wave (crest) in a given interval of time.
\[Speed=\frac{Distance}{Time}\]
Speeds of Different Types of Waves
The speed of a wave is different in a different medium. It can be determined by the type of wave and the physical properties of the medium in which it travels. An exception is found in the electromagnetic waves as they can travel through a vacuum. For most substances, the material will vibrate that will obey a Hooke's law force as a wave passes through it and the speed will not depend on frequency. Electromagnetic waves in a vacuum and waves travelling through a linear medium are termed linear waves and they have a constant speed.
Dependence Medium of the Wave Speed
The speed of most waves depends on the medium or the matter through which they travel. Usually, waves travel fastest in the solids and slowest in the gases. This is because particles are more close to each other in solids whereas farthest apart in gases. When the particles are farther apart, it takes a longer time for the energy distribution to pass from one particle to another through the medium.
Solved Examples
1.A Light Wave Travels With a Wavelength of 500 nm. Determine its Frequency.
Sol: Given, wavelength λ = 500 nm
We know the velocity of light (v) = 3 x 108 m/s2
The frequency is calculated by formula,
\[f=\frac{v}{\lambda }\]
Now put the value of v and λ in the above formula
\[f=\frac{3 \times10^{8}}{500 \times10^{-9} }\]
\[f=\frac{3 \times10^{8}}{5 \times10^{-7} }\]
f = 6 x 1014 Hz
Hence the frequency of the light wave is 6 x 1014 Hz
2. Wavelength of a Sound Wave is 1.5 nm. Determine its Frequency.
Sol: Given wavelength λ = 1.5 nm
As we know the velocity of sound wave (v) = 343.2 m/s
Frequency is calculated by the formula
\[f=\frac{v}{\lambda }\]
Now put the value of wavelength and velocity in the formula,
\[f=\frac{343.2}{1.5 \times10^{-9} }\]
f = 22.8 KHz
Hence the frequency of the sound wave is 22.8 kHz
Conclusion
Wave speed is the distance travelled by a wave travels in a given amount of time. For example the number of meters, it travels per second.
Wave speed is related to wavelength and wave frequency and it is given by the equation:
Speed = Wavelength x Frequency. This equation can be used to calculate wave speed when the wavelength and frequency value is known.
The equation for wave speed can be written to solve for wavelength or frequency if the speed and the other value are known.
The speed of most of the waves depends on the medium or the matter through which they travel. Generally, waves travel fastest through solids medium and slowest through gases medium.
FAQs on Wave Speed: Definition, Formula, and Concepts
1. What is a wave in Physics?
A wave is a disturbance that travels through a medium, transferring energy from one point to another without any net movement of the medium itself. For instance, in ocean waves, the water particles primarily move up and down while the wave energy travels forward across the sea.
2. How is wave speed defined and what is its formula?
Wave speed is the distance a wave travels in a specific amount of time, indicating how fast the disturbance moves. The fundamental relationship is expressed in the formula: Wave Speed (v) = Frequency (f) × Wavelength (λ). This measures how quickly a point on the wave, such as a crest, propagates through the medium.
3. What are the main types of waves?
Waves can be classified based on how their particles move and whether they need a medium to travel. The primary types are:
- Transverse Waves: The medium's particles move perpendicular to the direction of wave travel. Examples include light waves and ripples on water.
- Longitudinal Waves: The medium's particles move parallel to the direction of wave travel, creating compressions and rarefactions. Sound waves are a classic example.
- Mechanical Waves: These waves, like sound or seismic waves, require a physical medium to transfer energy.
- Electromagnetic Waves: These waves, such as light and radio waves, do not need a medium and can travel through the vacuum of space.
4. What is the SI unit for measuring wave speed?
The standard SI (International System of Units) for wave speed is metres per second (m/s). This is because speed is defined as the distance (measured in metres) travelled over a period of time (measured in seconds).
5. Why is understanding wave speed important in real life?
Understanding wave speed is crucial because it explains many natural phenomena and powers modern technology. For example, it clarifies why you see lightning instantly but hear the thunder later, as light waves travel much faster than sound waves. It is also fundamental to telecommunications, medical ultrasounds, and seismology for studying earthquakes.
6. How does the medium a wave travels through affect its speed?
The speed of a mechanical wave is determined by the properties of the medium it passes through, specifically its elasticity and density. Generally, waves travel faster in more elastic and denser media because the particles are closer together and can transfer energy more efficiently. This is why sound travels faster through solids than through liquids or gases.
7. What is the difference between wave speed and the speed of the particles in the wave?
This is a common point of confusion. Wave speed refers to how fast the overall wave pattern (the disturbance) moves through the medium. In contrast, particle speed describes how fast the individual particles of the medium oscillate around their fixed positions. The two speeds are distinct and are not the same.
8. Can the speed of a single wave change?
Yes, a wave's speed changes when it moves from one medium into another. This event is known as refraction. When this happens, the wave's frequency remains constant, but its wavelength and speed change to adapt to the new medium's properties. A simple example is seeing a straw appear bent in a glass of water, which is caused by light waves slowing down as they enter the water from the air.
