Question

A car is moving towards a high cliff. The car driver sounds a horn of frequency f. The reflected sound heard by the driver has a frequency 2f. If v be the velocity of sound, then the velocity of the car, in the same velocity units, will be:

Options

• `"v"/2`

• `"v"/sqrt2`

• `"v"/3`

• `"v"/4`

Answer 1

`"v"/3`

Explanation:

Let f' be the frequency of sound heard by the cliff.

∴ f' = `"vf"/("v" - "v"_"c")` ....(1)

Now for the reflected wave cliff acts as a source

∴ 2f' = `("f'"("v" + "v"_"c"))/"v"` .....(2)

2f = `(("v" + "v"_"c")"f")/("v" - "v"_"c")`

⇒ 2v − 2v_c

= v + v_c or `"v"/3` = v_c