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  4. Waves Chapter-Wise Test 2

Waves Chapter-Wise Test 2

Correct answer Carries: 4.

Wrong Answer Carries: -1.

Which property of a medium is most critical for the propagation of longitudinal waves through a gas?

Longitudinal waves in a gas rely on compressibility, quantified by the bulk modulus, which provides the restoring force for pressure oscillations, unlike shear modulus needed for transverse waves.

Bulk modulus
Shear modulus
Viscosity
Density
1

Two waves of frequencies 510 Hz and 514 Hz interfere. How many beats are heard in 15 seconds?

Beat frequency: \( v_{\text{beat}} = 514 - 510 = 4 \, \text{Hz} \).

Beats in 15 s: \( 4 \times 15 = 60 \).

50
55
60
65
3

A stationary wave on a string fixed at both ends has a frequency of 150 Hz and a wave speed of 45 m/s. What is the wavelength?

Wavelength: \( \lambda = \frac{v}{v} = \frac{45}{150} = 0.3 \, \text{m} \).

0.2 m
0.25 m
0.35 m
0.3 m
4

A transverse wave on a string has a tension of 180 N and a linear mass density of 0.03 kg/m. What is the wavelength if the frequency is 20 Hz?

Speed: \( v = \sqrt{\frac{T}{\mu}} = \sqrt{\frac{180}{0.03}} = \sqrt{6000} \approx 77.46 \, \text{m/s} \).

Wavelength: \( \lambda = \frac{v}{v} = \frac{77.46}{20} \approx 3.87 \, \text{m} \).

3.5 m
3.8 m
4 m
3.87 m
4

A pipe open at both ends has a length of 0.34 m and resonates with a source of frequency 1000 Hz. What is the harmonic number if the speed of sound is 340 m/s?

\( v_n = \frac{n v}{2L} \).

\( 1000 = \frac{n \times 340}{2 \times 0.34} = \frac{n \times 340}{0.68} \).

\( 1000 = n \times 500 \Rightarrow n = \frac{1000}{500} = 2 \).

Second harmonic.

1
2
3
4
2

A string of length 4 m and mass 0.08 kg is under a tension of 200 N. How long does a transverse pulse take to travel its length?

Linear mass density: \( \mu = \frac{0.08}{4} = 0.02 \, \text{kg/m} \).

Speed: \( v = \sqrt{\frac{T}{\mu}} = \sqrt{\frac{200}{0.02}} = \sqrt{10000} = 100 \, \text{m/s} \).

Time: \( t = \frac{\text{length}}{v} = \frac{4}{100} = 0.04 \, \text{s} \).

0.03 s
0.05 s
0.04 s
0.06 s
3

Two waves \( y_1 = 4 \sin (5x - 10t) \) and \( y_2 = 4 \sin (5x - 10t + \frac{\pi}{6}) \) interfere. What is the amplitude of the resultant wave?

Amplitude: \( A = 2a \cos \frac{\phi}{2} \), \( a = 4 \, \text{m} \), \( \phi = \frac{\pi}{6} \).

\( A = 2 \times 4 \cos \frac{\pi}{12} \approx 8 \times 0.966 = 7.73 \, \text{m} \).

4 m
7.7 m
8 m
6 m
2

A steel rod of length 1.5 m has a fundamental frequency of longitudinal vibrations of 2 kHz. What is the speed of sound in the rod?

For rod clamped at middle, fundamental: \( v_1 = \frac{v}{2L} \).

\( 2000 = \frac{v}{2 \times 1.5} \Rightarrow v = 2000 \times 3 = 6000 \, \text{m/s} \).

5000 m/s
5500 m/s
6000 m/s
6500 m/s
3

A pipe open at both ends has a length of 0.68 m and resonates with a source of frequency 750 Hz. What is the harmonic number if the speed of sound is 340 m/s?

\( v_n = \frac{n v}{2L} \).

\( 750 = \frac{n \times 340}{2 \times 0.68} = \frac{n \times 340}{1.36} \).

\( 750 = n \times 250 \Rightarrow n = \frac{750}{250} = 3 \).

Third harmonic.

2
3
4
5
2

A string of length 3 m and mass 0.06 kg is under a tension of 150 N. What is the speed of a transverse wave on the string?

Linear mass density: \( \mu = \frac{0.06}{3} = 0.02 \, \text{kg/m} \).

Speed: \( v = \sqrt{\frac{T}{\mu}} = \sqrt{\frac{150}{0.02}} = \sqrt{7500} \approx 86.6 \, \text{m/s} \).

86.6 m/s
80 m/s
90 m/s
100 m/s
1

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