Question

Two waves of wavelength 2.00 m and 2.02 m superpose with each other to produce beats in 1 s. If the speed of both waves is the same, their same speed is ..............(a) 400 m/s(b) 402 m/s(c) 404 m/s(d) 406 m/s

Answer 1

Answer:

their speed is -c) 404 m/s

Answer 2

Same speed of both waves is 201.999 m/s

Explanation:

Given,

Wavelength ,\lambda_1 = 2.0 mm

                     \lambda_2 = 2.02 mm

Produce beats, = 1 s

We know that,

$f_1 - f_2 = \frac{v}{\lambda_1} - \frac{v}{\lambda_2}$

$f_1 - f_2 = v \times \left ( \frac{1}{\lambda_1} - \frac{1}{\lambda_2} \right )$

Put the given values ,

$1 = v\times \left ( \frac{1}{\2.0} - \frac{1}{2.02} \right )$

$1 = v\times \left ( 0.5 - 0.49504950 \right )$

$1 = v\times 0.0049505$

$v = \frac{1}{0.0049505}$

v = 201.9998 m/s

Same speed of both waves is 201.999 m/s