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:

To find the time t, we use the fundamental wave relationship where wave speed (v) equals frequency (f) multiplied by wavelength (λ), expressed as v = fλ. Speed is also defined as the total distance covered divided by the time taken [1]. In this problem, the frequency (f) is 300 Hz, and the distance traveled is given as 150 times the wavelength (Distance = 150λ). Using the formula for time, t = Distance / Speed, we substitute the known values: t = (150λ) / (fλ). The wavelength (λ) cancels out from the numerator and denominator, leaving t = 150 / f. Substituting the given frequency of 300 Hz, we get t = 150 / 300, which simplifies to 0.5 seconds. Thus, the sound wave takes 0.5 seconds to travel a distance equal to 150 of its wavelengths regardless of the specific medium.

Sources

1. [1] Science-Class VII . NCERT(Revised ed 2025) > Chapter 8: Measurement of Time and Motion > 8.3 Speed > p. 113