[3 Mark Question Answer]

Question 13 Marks

The frequency of a source of sound is 100 Hz. How many times does it vibrate in a minute?

Answer

Frequency is defined as the number of oscillations per second. It is given by the relation:
$
\text { Frequency }=\frac{\text { Number of oscillations }}{\text { Total time }}
$
Number of oscillations $=$ Frequency $\times$ Total time

Given, Frequency of sound $=100 Hz$

Total time $=1 min =60 s$

Number of oscillations/Vibrations $=100 \times 60=6000$

Hence, the source vibrates 6000 times in a minute, producing a frequency of $100 Hz$.

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Question 23 Marks

Calculate the wavelength of a sound wave whose frequency is $220\ Hz$ and speed is $440\ m/s$ in a given medium.

Answer

Frequency of the sound wave, $v=220 Hz$
Speed of the sound wave, $v=440 m s ^{-1}$
For a sound wave,
$ \text { Speed }=\text { Wavelength } \times \text { Frequency }$
$v=\lambda \times v$
$\therefore \lambda=\frac{v}{v}=\frac{440}{220}=2 m $
Hence, the wavelength of the sound wave is $2 m$.

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Question 33 Marks

What are wavelength, frequency, time period and amplitude of a sound wave?

Answer

Wavelength:- The distance between two consecutive compressions or two consecutive rarefactions is known as the wavelength. Its SI unit is metre (m).
Frequency:- The number of complete oscillations per second is known as the frequency of a sound wave. It is measured in hertz (Hz).
Time Period:- The time taken by two consecutive compressions or rarefactions to cross a fixed reference point is called the time period (T) of the wave.
Amplitude:- The maximum height reached by the crest or trough of a sound wave is called its amplitude

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Question 43 Marks

How are the wave velocity V, frequency f and wavelength λ of a wave related? Derive the relationship.

Answer

Let the velocity of a wave be V, time period T, frequency ν and wavelength λ. By the definition of wavelength,
Wavelength = Distance travelled by the wave in one time period i.e., in T second
Or, wavelength = Wave velocity x Time period
Or, λ = V x T
Or,λ = V x 1/ ν [As, T = 1/]
Therefore, V = ν λ
Therefore, Wave velocity = Frequency x wavelength

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Question 53 Marks

Explain the terms crest and trough in relation to a transverse wave.

Answer

A crest is a point on the transverse wave where the displacement of the medium is at a maximum.
A point on the transverse wave is a trough if the displacement of the medium at that point is at a minimum.

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Question 63 Marks

How long will sound take to travel in (a) and iron rail and (b) air, both 3.3 km in length? Take speed of sound in air to be 330 m/s and in iron to be 5280 m/s.

Answer

(a) Length of iron rail (D) = 3.3 km = 3300 m
Speed of sound in iron (V) = 5280 m/s
Time taken by sound to travel in iron rod (t) = D/V
Or, t = (3300 / 5280) s = 0.625 s
(b) Length of iron rail (D) = 3.3 km = 3300 m
Speed of sound in air (V) = 330 m/s
Time taken by sound to travel in iron rod (t) = D/V
Or, t = (3300/330) s = 10 s

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