Sound Solved Examples (9 Physics)
Sound is a mechanical wave that travels through different media. These examples cover speed of sound, frequency, wavelength, echo, and the Doppler effect w
TL;DR: Sound is a mechanical wave that travels through different media. These examples cover speed of sound, frequency, wavelength, echo, and the Doppler eff…
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Sound is a mechanical wave that travels through different media. These examples cover speed of sound, frequency, wavelength, echo, and the Doppler effect w
Sound — Solved Numerical Examples (Step by Step)
Example 1: A sound wave travels at 340 m/s in air. If the frequency is 100 Hz, find the wavelength.
Solution: Given: Speed of sound v = 340 m/s, Frequency f = 100 Hz
Use the relationship: v = f × λ
Where λ is wavelength
340 = 100 × λ
λ = 340 / 100 = 3.4 m
Example 2: A person claps in front of a cliff and hears the echo after 2 seconds. What is the distance of the cliff? (Speed of sound = 340 m/s)
Solution: The sound travels from the person to the cliff and back to the person.
Total distance traveled = 2 × distance to cliff
Speed = distance / time
Total distance = speed × time = 340 × 2 = 680 m
Distance to cliff = 680 / 2 = 340 m
Alternatively: Time for sound to go and return = 2 s
Time to go one way = 2 / 2 = 1 s
Distance = 340 × 1 = 340 m
Example 3: The frequency of a sound wave is 50 Hz and wavelength is 6.8 m. Find the speed of sound in that medium.
Solution: Given: Frequency f = 50 Hz, Wavelength λ = 6.8 m
Use the relationship: v = f × λ
v = 50 × 6.8 = 340 m/s
Example 4: A train whistle has a frequency of 400 Hz. An observer on the train hears it. What is the period of the sound wave?
Solution: Given: Frequency f = 400 Hz
Period T is the reciprocal of frequency.
T = 1 / f = 1 / 400 = 0.0025 s = 2.5 × 10^-3 s = 2.5 ms
Period is the time taken for one complete oscillation.
Example 5: A person is at a distance of 680 m from a cliff. They make a loud sound. How long after making the sound will they hear the echo? (Speed of sound = 340 m/s)
Solution: The sound travels from the person to the cliff and back.
Total distance = 680 + 680 = 1360 m
Speed of sound = 340 m/s
Time = distance / speed = 1360 / 340 = 4 s
Example 6: The speed of sound in water is 1480 m/s. A dolphin emits a sound of frequency 120 Hz. Find the wavelength of the sound in water.
Solution: Given: Speed in water v = 1480 m/s, Frequency f = 120 Hz
Use v = f × λ
1480 = 120 × λ
λ = 1480 / 120 = 12.33 m (approximately)
Example 7: A sound wave has a wavelength of 2 m and travels at 340 m/s. How many complete waves pass a point in one second?
Solution: Given: Wavelength λ = 2 m, Speed v = 340 m/s
We need to find frequency f.
v = f × λ
340 = f × 2
f = 340 / 2 = 170 Hz
Frequency of 170 Hz means 170 complete waves pass a point in one second.
Tips
- Remember v = f × λ: speed equals frequency times wavelength.
- Period T = 1/f: period is the reciprocal of frequency.
- Echo occurs when sound reflects back; total distance is twice the distance to the reflecting surface.
- Different media have different speeds of sound: speed in water > speed in air > speed in gases.
Frequently Asked Questions
Why does sound travel faster in water than in air?
Sound travels faster in denser media because molecules are more tightly packed, allowing vibrations to transmit more efficiently. Water is denser than air, so sound travels at about 1480 m/s in water versus 340 m/s in air.
What is the relationship between frequency, wavelength, and speed?
The speed of sound in a medium is constant for that medium. If frequency increases, wavelength must decrease to keep speed constant. This relationship is expressed as v = f × λ.
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