A sound wave having frequency of 300 Hz is travelling in an unknown me

A sound wave having frequency of 300 Hz is travelling in an unknown medium. Its wavelength is not known. It travels a distance equal to 150 times its wavelength in time t. The value of t is :

0.5 s
1 s
1.5 s
2 s
This question was previously asked in
UPSC CDS-2 – 2024
The time taken for the sound wave to travel the given distance is 0.5 s.
– The speed of a wave (v) is given by the product of its frequency (f) and wavelength (λ): v = f * λ.
– The distance travelled (d) is given as 150 times the wavelength: d = 150λ.
– The relationship between speed, distance, and time (t) is v = d / t.
– Combining these equations, we get: f * λ = (150λ) / t.
– We can cancel out λ from both sides (assuming λ is non-zero): f = 150 / t.
– We are given the frequency f = 300 Hz.
– Rearranging the equation to find t: t = 150 / f.
– Substituting the value of f: t = 150 / 300 = 0.5 s.
This calculation assumes the speed of the sound wave is constant in the unknown medium. The wavelength of the sound wave in the medium is not required to find the time, as it cancels out in the calculation.