Question

A sound wave traveling through a certain freshwater lake has a frequency of 349.2 Hz and a wavelength of 4.25 m. What is the speed of a sound wave in this water? (Round your answer to three significant figures.)

Answer 1

Answer:

ν = 1483.939 m/s

Explanation:

Wave propagation speed (ν):

• ν = λ / T

∴ Wavelength ( λ ) = 4.25 m

∴ Period ( T ) = 1 / f

∴ frequency ( f ) = 349.2 Hz ( s-1 )

⇒ T = 1 / 349.2 s-1

⇒ T = 2.864 E-3 s

⇒ ν = (4.25 m) / (2.864 E-3 s)

⇒ ν = 1483.939 m/s

Answer 2

Answer: The wave speed of the given sound wave is $1.48\times 10^3m/s$  

Explanation:

Wave speed is defined as the product of its wavelength and frequency.

Mathematically,

$\text{Wave speed}=\lambda\times \nu$

where,

$\lambda$ = wavelength of the wave = 4.25 m

$\nu$ = frequency of the wave = 349.2 Hz = $349.2s^{-1}$

Putting values in above equation, we get:

$\text{Wave speed}=4.25m\times 349.2s^{-1}\\\\\text{Wave speed}=1484.1m/s=1.48\times 10^3m/s$

Hence, the wave speed of the given sound wave is $1.48\times 10^3m/s$