The following equations represent progressive transverse waves ${Z}_{1}=A\mathrm{cos}\left(\omega \text{\hspace{0.17em}}t-kx\right)$, ${Z}_{2}=A\mathrm{cos}\left(\omega \text{\hspace{0.17em}}t+kx\right)$, ${Z}_{3}=A\mathrm{cos}\left(\omega \text{\hspace{0.17em}}t+ky\right)$ and ${Z}_{4}=A\mathrm{cos}\left(2\omega \text{\hspace{0.17em}}t-2ky\right)$. A stationary wave will be formed by superposing :

(1) Z1 and Z2

(2) Z1 and Z4

(3) Z2 and Z3

(4) Z3 and Z4

Concept Questions :-

Standing waves
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Two traveling waves ${y}_{1}=A\mathrm{sin}\left[k\left(x-c\text{\hspace{0.17em}}t\right)\right]$ and ${y}_{2}=A\mathrm{sin}\left[k\left(x+c\text{\hspace{0.17em}}t\right)\right]$ are superimposed on the string. The distance between adjacent nodes is :

(1) ct / π

(2) ct / 2π

(3) π / 2k

(4) π / k

Concept Questions :-

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

(1) $\frac{l}{4}$

(2) $\frac{l}{2}$

(3) l

(4) 2l

Concept Questions :-

Standing waves
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A 1 cm long string vibrates with the fundamental frequency of 256 Hz. If the length is reduced to $\frac{1}{4}cm$  keeping the tension unaltered, the new fundamental frequency will be :

(1) 64

(2) 256

(3) 512

(4) 1024

Concept Questions :-

Travelling wave on string
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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 :

(1) 2 Hz

(2) 4 Hz

(3) 5 Hz

(4) 10 Hz

Concept Questions :-

Standing waves
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A string is producing transverse vibration whose equation is $y=0.021\text{\hspace{0.17em}}\mathrm{sin}\left(x+30t\right)$, 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 :

(1) 10

(2) 0.5

(3) 1

(4) 0.117

Concept Questions :-

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

(1) $\lambda =\frac{{n}^{2}}{2l}$

(2) $\lambda =\frac{{l}^{2}}{2n}$

(3) $\lambda =\frac{2l}{n}$

(4) $\lambda =2l\text{\hspace{0.17em}}n$

Concept Questions :-

Standing waves
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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 :

(1) 13.5 cm

(2) 2.7 cm

(3) 5.4 cm

(4) 10.3 cm

Concept Questions :-

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

(1) 5 N

(2) 20 N

(3) 40 N

(4) 80 N

Concept Questions :-

Travelling wave on string
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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 :

(1) 77 m/s

(2) 102 m/s

(3) 110 m/s

(4) 165 m/s

Concept Questions :-

Travelling wave on string
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