A standing wave is represented by

Y=Asin(100t)cos(0.01x)

where Y and A are in millimetre, t is in seconds and x is in metre. The velocity of the wave is :

(1) 104 m/s

(2) 1 m/s

(3) 10–4 m/s

(4) Not derivable from the above data

Concept Questions :-

Standing waves
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Two waves are approaching each other with a velocity of 20 m/s and frequency n. The distance between two consecutive nodes is :

(1) 20n

(2) 10n

(3) 5n

(4) n10

Concept Questions :-

Standing waves
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The stationary wave produced on a string is represented by the equation y=5cos(πx/3)sin40πt where x and y are in cm and t is in seconds. The distance between consecutive nodes is :

1. 5 cm

2. π cm

3. 3 cm

4. 40 cm

Concept Questions :-

Standing waves
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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 :

(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 y1=Asin[k(xct)] and y2=Asin[k(x+ct)] 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) l4

(2) l2

(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 14cm  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=0.021sin(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 :

(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) λ=n22l

(2) λ=l22n

(3) λ=2ln

(4) λ=2ln

Concept Questions :-

Standing waves
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