Physics Test

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Physics Test - 4

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Weekly Quiz Competition

Question 1
4 / -0.83

The equation of a wave disturbance is given as :
where X and y are in metres and t in seconds. Choose the wrong statement:

A
Node occurs at x = 0.15 m

B
The wavelength is 0.2 m

C
Antinode occurs at x = 0.3 m

D
The speed of the constituent waves is 5 m/s

Solution

y=0.02cos(π/2+50 π∗t)cos(10 π∗x)
At x=0.3m
y=0.02cos(π/2+50 π∗t)cos(3 π) = −0.02cos(π/2+50 π∗t) (It is right)
Now compare the given equation by the standard stationary wave equation,
y=Acos(ϕ+ω∗t)cos(2 π/λ∗x)
2 π/λ=10 π, λ=0.2m (it is also right)
At x=0.15m,
y=0.02cos(π/2+50 π∗t)cos(π/2),
and
v=A ω=0.02 ∗50 π=πms⁻¹
so option d is incorrect.
Question 2
4 / -0.83

In a plane progressive harmonic wave particle speed is always less than the wave speed if:
(where A is wavelength of wave)

A

B

C
amplitude of wave is greater than

D

Solution

Let equation of a plane progressive harmonic wave be

wave speed
and maximum particle speed
Given that v_p
The Correct answer is : amplitude of wave is less than
Question 3
4 / -0.83

Which of the following is not the standard form of a sine wave?

A

B

C

D

Solution

Standard form of a sine wave is

With these substitutions we can see that Equation (1) can be written as options (b).
The correct answer is:
Question 4
4 / -0.83

Two sound source are moving in opposite directions with velocities v₁ and v₂ (v₁ >v₂ ). Both are moving away from a stationary observer. The frequency of both the sources is 900 Hz. What is the value of v₁ - v₂ so that the beat frequency observed by the observer is 6 Hz. Speed of sound v = 300 mis. Given, that v₁ and v₂ «v.

A
4 m/s

B
3 m/s

C
1 m/s

D
2 m/s

Solution

The correct answer is: 2 m/s
Question 5
4 / -0.83

String 1 has twice the length, twice the radius, twice the tension and twice the density of another string 2. The relation between the fundamental frequencies of 1 and 2 is :

A
f₁ = f₂

B
f₁ = 2f₂

C
f2 = 4f1

D
f₁ = 4f₂

Solution

(m = mass per unit length =pS)

The correct answer is: f₂ = 4f₁
Question 6
4 / -0.83

A string of length L is stretched by L/20 and speed of transverse wave along it is v. The speed of wave when it is stretched by L/10 will be : (assume the Hooke ’s law is applicable)

A
√2v

B
4v

C
2v

D

Solution

The correct answer is: √2v
Question 7
4 / -0.83

Speed of transverse wave in a string of density 100 kglm³ and area of cross-section 10 mm² under the tension of 10³ N is :

A
200 m/s

B
1000 m/s

C
2000 m/s

D
100 m/s

Solution

Here, m = mass per unit length = pS

The correct answer is: 1000 m/s
Question 8
4 / -0.83

A wave represented by the equation y1 = Acos(kx- ωt), is superimposed with another wave to form a stationary wave such that the point x = 0 is a node. The equation of the other wave is :

A

B

C

D

Solution

y=y₁ + y₂
At x = 0, y = 0 for all values of t only when

The correct answer is:
Question 9
4 / -0.83

The frequency changes by 10% as the source approaches a stationary observer with constant speed v_s . What would be the percentage change in frequency as the source recedes the observer with the same speed ? Given, that v_s «v ( v = speed of sound in air)

A
16.7%

B
8.5%

C
14.3%

D
20%

Solution
Question 10
4 / -0.83

A heavy rope is suspended from a rigid support. A wave pulse is set up at the lower end, then :

A
the pulse will travel with decreasing speed

B
the pulse will travel with increasing speed

C
the pulse will travel with uniform speed

D
the pulse cannot travel through the rope

Solution

Due to weight of the rope, the tension will increase along the rope from the lower end to the upper end. Hence, the pulse will travel with increasing speed as

The correct answer is: the pulse will travel with increasing speed