1. A source and an observer move away from each other, with a velocity of 10m/s with respect to ground. If the observer finds the frequency of sound coming from the source as 1950 Hz, then original frequency of source is (velocity of sound in air = 340 m/s)

1. 1. 1950 Hz

   
   
   

   2. 2068 Hz

   
   
   

   3. 2132 Hz

   
   
   

   4. 2486 Hz

   
   
   

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1. View Hint View Answer Discuss in Forum

   According to Doppler's effect
   

   n' =

   v - v0

   n =

   340 - 10

   n =

   330

   × 1950 = 2068 Hz

   v - vs

   340 + 10

   350

   Correct Option: B

   According to Doppler's effect
   

   n' =

   v - v0

   n =

   340 - 10

   n =

   330

   × 1950 = 2068 Hz

   v - vs

   340 + 10

   350

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2. A car is moving towards a high cliff. The car driver sounds a horn of frequency ƒ. The reflected sound heard by the driver has  frequency 2ƒ. If v be the velocity of sound, then the velocity of the car, in the same velocity units, will be

1. 1. v/2

   
   
   

   2. v/√2

   
   
   

   3. v/3

   
   
   

   4. v/4

   
   
   

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1. View Hint View Answer Discuss in Forum

   Let ƒ' be the frequency of sound heard by cliff.
   

   ∴ ƒ =	vƒ	..........(1)
   	v - vc

   
   Now, for the reflected wave, cliff acts as a source,
   

   ∴ 2ƒ =	ƒ(v + vc)	..........(2)
   	v

   
   

   2ƒ =	(v + vc)ƒ
   	v - vc

   
   ⇒ 2v - 2v_c = v + v_c or v/3 = v_c

   Correct Option: C

   Let ƒ' be the frequency of sound heard by cliff.
   

   ∴ ƒ =	vƒ	..........(1)
   	v - vc

   
   Now, for the reflected wave, cliff acts as a source,
   

   ∴ 2ƒ =	ƒ(v + vc)	..........(2)
   	v

   
   

   2ƒ =	(v + vc)ƒ
   	v - vc

   
   ⇒ 2v - 2v_c = v + v_c or v/3 = v_c

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3. The equation of a wave is represented by:
   

   y = 104sin		100 ƒ +	x
   			10

   
   The velocity of the wave will be

1. 1. 100 m/s

   
   
   

   2. 250 m/s

   
   
   

   3. 750 m/s

   
   
   

   4. 1000 m/s

   
   
   

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1. View Hint View Answer Discuss in Forum

   y = 10-4 sin		100t -	x
   			10

   
   ν = 100 sec^–1, λ = 10 m
   v = λν = 10 × 100 = 1000 m/s

   Correct Option: D

   y = 10-4 sin		100t -	x
   			10

   
   ν = 100 sec^–1, λ = 10 m
   v = λν = 10 × 100 = 1000 m/s

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4. A transverse wave propagating along x-axis is represented by y(x,t) = 8.0 sin(0.5 πx - 4πt - π/4) where x is in metres and t is in seconds. The speed of the wave is

1. 1. 0.5 π m/s

   
   
   

   2. π/4 (m/s)

   
   
   

   3. 8 m/s

   
   
   

   4. 4π m/s

   
   
   

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1. View Hint View Answer Discuss in Forum

   Speed of a wave represented by the equation
   y(x, t) = A sin (kx – ωt + φ) is v = ω/k
   By comparison, ω = 4π; k = 0.5π
   

   v =	ω	=	4π	= 8 m/sec
   	k		0.5π

   Correct Option: C

   Speed of a wave represented by the equation
   y(x, t) = A sin (kx – ωt + φ) is v = ω/k
   By comparison, ω = 4π; k = 0.5π
   

   v =	ω	=	4π	= 8 m/sec
   	k		0.5π

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5. A transverse wave is represented by y = A sin (t–kx). For what value of the wavelength is the wave velocity equal to the maximum particle velocity?

1. 1. πA/2

   
   
   

   2. πA

   
   
   

   3. 2πA

   
   
   

   4. A

   
   
   

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1. View Hint View Answer Discuss in Forum

   y = A sin (ωt–kx)
   Particle velocity,
   

   vp =	dy	A ω cos(ωt - kx)
   	dt

   
   v_{p max} = Aω
   wave velocity = ω/k
   ∴ Aω = ω/k
   

   i.e., A =	1	But k =	2π
   	k		λ

   
   ∴ λ = 2πA

   Correct Option: C

   y = A sin (ωt–kx)
   Particle velocity,
   

   vp =	dy	A ω cos(ωt - kx)
   	dt

   
   v_{p max} = Aω
   wave velocity = ω/k
   ∴ Aω = ω/k
   

   i.e., A =	1	But k =	2π
   	k		λ

   
   ∴ λ = 2πA

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