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Transverse wave of amplitude 10 cm is generated at one end (x = 0) of a long string by a tuning fork of frequency 500 Hz. At a certain instant of time, the displacement of a particle A at x = 100 cm is -5 cm and of particle B at x = 200 cm is +5 cm. What is the wavelength of the wave?
  • a)
    2 m
  • b)
    3 m
  • c)
    4 m
  • d)
    5 m
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
Transverse wave of amplitude 10 cm is generated at one end (x = 0) of ...
Given data:
Amplitude (A) = 10 cm
Frequency (f) = 500 Hz
Displacement at x = 100 cm, particle A (yA) = -5 cm
Displacement at x = 200 cm, particle B (yB) = 5 cm

To find:
Wavelength (λ) of the wave

Formula:
The equation of a transverse wave is given by:
y = A sin (2πft)

Where,
y is the displacement of the particle at a given position and time,
A is the amplitude of the wave,
f is the frequency of the wave,
t is the time, and
2π is a constant.

Steps to solve the problem:

1. Determine the time period (T) of the wave using the formula:
T = 1/f

Substituting the given frequency, we have:
T = 1/500 Hz
T = 0.002 s

2. Find the phase difference (φ) between particles A and B using the formula:
φ = 2π(xB - xA)/λ

Where,
xB is the position of particle B,
xA is the position of particle A, and
λ is the wavelength of the wave.

Substituting the given positions, we have:
φ = 2π(200 cm - 100 cm)/λ
φ = 2πλ/λ
φ = 2π

3. Determine the phase difference (θ) at the given instant using the formula:
θ = 2πft

Substituting the given frequency, we have:
θ = 2π(500 Hz)(0.002 s)
θ = 2π

4. Equate the phase differences:
φ = θ

2π = 2π

This means that the phase difference between particles A and B is equal to the phase difference at the given instant.

5. The phase difference of 2π corresponds to one complete wave or wavelength. Therefore, the wavelength (λ) of the wave is equal to the distance between particles A and B.
λ = xB - xA
λ = 200 cm - 100 cm
λ = 100 cm

Converting the wavelength to meters:
λ = 100 cm * (1 m / 100 cm)
λ = 1 m

Therefore, the wavelength of the wave is 1 m, which corresponds to option A.
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Transverse wave of amplitude 10 cm is generated at one end (x = 0) of ...
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Transverse wave of amplitude 10 cm is generated at one end (x = 0) of a long string by a tuning fork of frequency 500 Hz. At a certain instant of time, the displacement of a particle A at x = 100 cm is -5 cm and of particle B at x = 200 cm is +5 cm. What is the wavelength of the wave?a)2 mb)3 mc)4 md)5 mCorrect answer is option 'A'. Can you explain this answer?
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