Question

Two waves of wavelength 2 m and 2.02 m, with the same speed superimpose to produce 2 beats per second. The speed of each wave is ____________.

Options

• 400 ms^-1

• 402 ms^-1

• 404 ms^-1

• 406 ms^-1

Answer 1

Two waves of wavelength 2 m and 2.02 m, with the same speed superimpose to produce 2 beats per second. The speed of each wave is 404 ms^-1.

Explanation:

`"n"_1 = "v"/lambda_1  "and"  "n"_2 = "v"/lambda_2`

`lambda_1 = 2  "m", lambda_2 = 2.02  "m"`

`"Since"   lambda_1 < lambda_2, "so"   "n"_1 > "n"_2`

`therefore "n"_1 - "n"_2 = 2`

`therefore "v"/lambda_1 - "v"/lambda_2 = 2`

`therefore "v"((lambda_2 - lamda_1)/(lambda_1 lambda_2)) = 2`

`therefore "v" = (2 xx lambda_1 lambda_2)/(lambda_2 - lambda_1)`

`= (2 xx 2 xx 2.02)/(2.02 - 2)`

` = 404  "m/s"`