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The contituent wave of a stationary wave have amplitude, frequency and velocity as 8 cm, 25 Hz and 150 cm/s respectively. What is the amplitude of the stationary wave at x = 2 cm ?

The contituent wave of a stationary wave have amplitude, frequency and velocity as 8 cm, 25 Hz and 150 cm/s respectively. What is the amplitude of the stationary wave at x = 2 cm ?

Grade:11

2 Answers

Arun
25763 Points
2 years ago
The question can be solved by drawing a graph or either by usin the below stated method :
Find the wavelength of the wave 
Velocity = Wavelength × Frequency
150 cm/s = Wavelength × 25 Hz
Wavelength = 150 ÷ 25
=> Wavelength = 6 cm
A CREST AND A TROUGH MAKE ONE WAVELENGTH
On comparing with the sine wave, 
180° = 6 cm and
hence value of 1 I.e. maximum value = 8 cm
=> 60° = 2cm
=> sin 60° = root (3) / 2
if 1 = 8cm
=> { sqrt (3) / 2 }= 8 × sqrt (3) / 2 cm
=> at x = 2cm 
Amplitude = 4 × sqrt (3)
 
 
Regards
Arun (askIITians forum expert)
Abhishek Dogra
34 Points
2 years ago
But the answer is 8√3 ,..............................................................................

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