Question

A sound wave has a frequency of 1500 Hz andwavelength 25 cm. How long will it take to travel 3 km?​

Answer 1

Solution :

⏭ Given:

✏ Frequency of sound wave = 1500Hz

✏ Wavelength = 25cm

✏ Distance covered = 3km

⏭ To Find:

✏ Time requires to cover the given distance.

⏭ Formula:

✏ Relation between frequency, wave velocity and wavelength is given by

$\bigstar \sf \: { \boxed{\tt{ \pink{frequency = \frac{velocity}{wavelength}}}}} \: \bigstar$

✏ Relation between velocity, distance and time is given by

$\bigstar \: \boxed{ \tt{ \green{ velocity = \dfrac{distance}{time}}}} \: \bigstar$

⏭ Conversation:

• 25 cm = 0.25 m
• 3 km = 3000 m

⏭ Calculation:

____________________________

$\implies \sf \: \red{ \nu = \dfrac{v}{ \lambda} = \dfrac{d}{ \lambda \times t} } \\ \\ \implies \sf \: 1500 = \dfrac{3000}{0.25 \times t} \\ \\ \implies \sf \: t = \dfrac{3000}{1500 \times 0.25} \\ \\ \implies \: \boxed{ \tt{ \large{ \purple{t = 8 \: sec}}}}$

____________________________

⏭ Additional information:

• Velocity is defined as ratio of distance covered to the total times.
• Wavelength is defined as distance covered by wave in time equal to time period.
• Time period is defined as time requires to complete one oscillation.

Answer 2

AnswEr:

$\boxed{\sf{\red{Time\:Taken\:=\:8\:s}}}$

ExplanaTion:

Given :

• Frequency = 1500 Hz
• Wavelength = 25 cm $\implies$ 0.25 m
• Distance = 3 km $\implies$ 3000 m

To find :

• Time taken to travel 3 km by a sound wave.

Solution :

We know that,

$\large{\boxed{\sf{\green{Frequency\:=\:\dfrac{Velocity}{Wavelength}}}}}$

Also,

Velocity = $\sf{\dfrac{Distance}{Time}}$

$\therefore$ $\large{\boxed{\sf{\purple{frequency\:=\:\dfrac{distance}{Wavelength\: \times time}}}}}$

Putting the values,

$\longrightarrow$ 1500 = $\sf{\dfrac{3000}{0.25 \times t}}$

$\longrightarrow$ t = 8 s

$\therefore$ $\boxed{\sf{\red{Time\:Taken\:=\:8\:s}}}$