Sample Problems on Sound Waves

Problem 1: An echo is heard after 4 s. What is the distance of the reflecting surface from the source given that the speed of sound is 284 m/s?

Solution:

Given,

Speed of sound (v) = 284 m/s and

Echo returns in time (t) = 4 s

Therefore,

The distance traveled by sound:

d = v × t 

⇒ d = 284 m/s × 4 s 

⇒ d = 1136 m

Since, Sound has to travel a distance that is twice the distance of the reflecting surface and the source.

Hence, the distance of the reflecting surface from the source, 

D = 1136 m / 2  

⇒ D = 568 m

Problem 2: A person clapped his hands near a cliff and heard the echo after 3 s. What is the distance of the cliff from the person if the speed of the sound is taken as 348 m/s?

Solution:

Given,

Speed of sound, v = 348 m/s and

Time taken for hearing the echo, t = 3 s.

Distance traveled by the sound,  

d = v × t 

⇒ d = 348 m/s × 3 s 

⇒ d = 1044 m 

In 2 s sound has to travel twice the distance between the cliff and the person.

Hence, the distance between the cliff and the person,

D = 1044 m / 2 

⇒ D = 522 m

Problem 3: Explain how defects in a metal block can be detected using ultrasound.

Solution:

Ultrasound waves have a high frequency. They can travel in mediums even with obstacles. Ultrasound waves can be transmitted through a metal block, if a defect is present then either its speed will change due to the defect or the wave will reflect back completely and will be detected by the detector. If no defect is found then the sound comes out at the expected velocity.

Problem 4: A sound wave has a frequency of 4 kHz and wavelength 35 cm. How long will it take to travel 2.5 km?

Solution:

Given,

Frequency (ν) = 4 kHz = 4000 Hz

Wavelength (λ) = 35 cm = 0.35 m

We know that, 

The speed of the wave = wavelength × frequency

v = λ ν 

⇒ v = 0.35 m × 4000 Hz 

⇒ v = 1400 m/s

The time taken by the wave to travel a distance of 2.5 km,

t = 2500 / 1400 

⇒ t =1.78 s

Thus, the sound will take 1.78 s to travel a distance of 2.5 km.

Problem 5: A body is vibrating 48000 times in one minute. If the velocity of sound in air is 360 m/s, find:

(a) Frequency of vibration in hertz,

(b) Wavelength of the wave produced.

Solution:

(a) Given,

Number of vibration in one minute = 48000

Number of vibrations in one sec =48000/60 = 800Hz

Therefore, Frequency (f)= 800 Hz

(b) Given,

Velocity of speed in air (v) = 360 m/s

Frequency (f) = 800 Hz

v = f λ

or λ = v / f

⇒ λ = 360 / 800 

⇒ λ = 0.45 m

Speed of Sound as the name suggests is the speed of the sound in any medium. We know that sound is a form of energy that is caused due to the vibration of the particles and sound travels in the form of waves. A wave is a vibratory disturbance that transfers energy from one point to another point without the actual transfer of matter. Hence, when we speak the sound from our vocal cords reaches to listener’s ear in the form of a wave.

Since the sound travels from the source point to the destination point within a time period, this encourages us to calculate the speed of the sound with which it travels. Also, we know that Sound is a mechanical wave hence its speed of propagation varies in different materials. In this article, we will learn, what is sound, what is the definition of Speed of Sound and the Speed of Sound with which it propagates in different media.