Question

A sound wave has ferquency of 3khz and a wavelength 45 cm .How long will it take to travel 1.8km?

Answer 1

Given that,

Frequency $(\nu)$ = 3 kHz

Wavelength $(\lambda)$ = 45 cm

Distance (s) = 1.8 km

To find,

Time taken to travel 1.8 km = ?

Now, first of all, we have to convert all the measurements into there SI units.

As we know,

(i) 1 kHz = 1000 Hz

∴ 3 kHz = 3000 Hz

(ii) 1 cm = 0.01 m

∴ 45 cm = 0.45 m

(iii) 1 km = 1000 m

∴ 1.8 km = 1800 m

Now, we'll calculate the velocity of the sound wave.

We know that,

Speed (v) = Frequency $\times$ Wavelength

Speed (v) = $\nu \times \lambda$

Speed (v) = $3000\:Hz \times 0.45\:m$

Speed (v) = 1,350 m/s

Now, we gotta the speed. Now, we'll calculate the time.

Take distance as 1800 m.

We know that,

Speed = $\frac{Distance\:(s)}{Time\:(t)}$

∴ time (t) = Distance (s) $\times$ Speed (v)

∴ time (t) = 1800 m $\times$ 1,350 m/s

∴ Time (t) = 2,430,000 seconds.