Waves MCQs for NEET — Physics Questions with Answers

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The following equations represent progressive transverse waves Z1=Acos(ωtkx), Z2=Acos(ωt+kx), Z3=Acos(ωt+ky) and Z4=Acos(2ωt2ky). A stationary wave will be formed by superposing :

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Explanation

When two waves of equal frequency and traveling in the opposite direction superimpose, then the stationary wave is produced. Hence Z1 and Z2 produce stationary waves.

Two traveling waves y1=Asin[k(xct)] and y2=Asin[k(x+ct)] are superimposed on the string. The distance between adjacent nodes is :

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Explanation

The distance between adjacent nodes x=λ2

Also, k=2πλ.

Hence, x=πk.

A string fixed at both ends is vibrating in two segments. The wavelength of the corresponding wave is :

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Explanation

When a string fixed at both ends vibrates in two segments, it means there is one node at the center. The wavelength of the standing wave is twice the length of the string segment, which is equal to the full length of the string (l).

A 1 cm long string vibrates with the fundamental frequency of 256 Hz. If the length is reduced to 14cm  keeping the tension unaltered, the new fundamental frequency will be :

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Explanation

n1ln2n1=l1l2

n2=l1l2n1=1×2561/4=1024Hz

Standing waves are produced in a 10 m long stretched string. If the string vibrates in 5 segments and the wave velocity is 20 m/s, the frequency is :

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Explanation

String vibrates in five segment so 52λ=lλ=2l5

Hence n=vλ=5×v2l=5×202×10=5 Hz

A string is producing transverse vibration whose equation is y=0.021sin(x+30t), Where x and y are in meters and t is in seconds. If the linear density of the string is 1.3×10–4 kg/m, then the tension in the string in N will be :

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Explanation

y=0.021sin(x+30t)v=ωk=301=30m/s.

Using, v=Tm30=T1.3×104T=0.117N

A stretched string of length l, fixed at both ends can sustain stationary waves of wavelength λ, given by 

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Explanation

λ=2lp (p = Number of loops)

A string on a musical instrument is 50 cm long and its fundamental frequency is 270 Hz. If the desired frequency of 1000 Hz is to be produced, the required length of the string is :

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Explanation

n1ll2l1=n1n2l2=l1n1n2=50×2701000=13.5cm

The tension in a piano wire is 10N. What should be the tension in the wire to produce a note of double the frequency :

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Explanation

nTn1n2=T1T2

n2n=10T2T2=40N

A string of 7 m length has a mass of 0.035 kg. If the tension in the string is 60.5 N, then the speed of a wave on the string is :

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Explanation

v=Tmv=60.5(0.035/7)=110 m/s

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