Question

A sound wave has a frequency of 3 kHz and wavelength 25 cm. The time taken by it to travel a distance of 1.5 km is :​

Answer 1

GIVEN :–

• Frequency of sound = 3 kHz = 3 × 10³ Hz

• Wavelength = 25 cm = 0.25 m

TO FIND :–

• The time taken by it to travel a distance of 1.5 km = ?

SOLUTION :–

• We know that –

$\\ \dashrightarrow \: \large{\boxed { \bold{Velocity \: \: of \: \: sound = Frequency \times Wavelength}}}$

• Put the values –

$\\ \implies { \bold{Velocity \: \: of \: \: sound = (3 \times {10}^{3} ) \times (0.25)}}$

$\\ \implies { \bold{Velocity \: \: of \: \: sound = (30 ) \times (25)}}$

$\\ \implies { \bold{Velocity \: \: of \: \: sound = 750 \: \dfrac{m}{s} }}$

▪︎ We also know that –

$\\ \implies{ \boxed { \bold{Velocity = \: \dfrac{Distance}{Time}} }}$

• So that –

$\\ \implies { \bold{750 = \: \dfrac{1.5 \times {10}^{3} }{Time}}}$

$\\ \implies { \bold{750 = \: \dfrac{1500}{Time}}}$

$\\ \implies { \bold{Time = \: \dfrac{1500}{750}}}$

$\\ \implies \large{ \boxed { \bold{Time =2 \: sec}}}$

Answer 2

$\huge{\mathbb{\red{ANSWER}}}$

$\huge{\mathbb{\red{Given}}}$

• Frequency of sound = 3 kHz = 3 × 10³ Hz

• Wavelength = 25 cm = 0.25 m

$\huge{\mathbb{\red{To find}}}$

• The time taken by it to travel a distance of 1.5 km = ?

$\huge{\mathbb{\red{solutions}}}$

• We know that –

$$\begin{lgathered}\\ \dashrightarrow \: \large{\boxed { \bold{Velocity \: \: of \: \: sound = Frequency \times Wavelength}}} \\\end{lgathered}$$

• Put the values –

$$\begin{lgathered}\\ \implies { \bold{Velocity \: \: of \: \: sound = (3 \times {10}^{3} ) \times (0.25)}} \\\end{lgathered}$$

$$\begin{lgathered}\\ \implies { \bold{Velocity \: \: of \: \: sound = (30 ) \times (25)}} \\\end{lgathered}$$

$$\begin{lgathered}\\ \implies { \bold{Velocity \: \: of \: \: sound = 750 \: \dfrac{m}{s} }} \\\end{lgathered}$$

▪︎ We also know that –

$$\begin{lgathered}\\ \implies{ \boxed { \bold{Velocity = \: \dfrac{Distance}{Time}} }} \\\end{lgathered}$$

$\huge{\mathbb{\red{Given}}}$

•

$$\begin{lgathered}\\ \implies { \bold{750 = \: \dfrac{1.5 \times {10}^{3} }{Time}}} \\\end{lgathered}$$

$$\begin{lgathered}\\ \implies { \bold{750 = \: \dfrac{1500}{Time}}} \\\end{lgathered}$$

$$\begin{lgathered}\\ \implies { \bold{Time = \: \dfrac{1500}{750}}} \\\end{lgathered}$$

$$\begin{lgathered}\\ \implies \large{ \boxed { \bold{Time =2 \: sec}}} \\\end{lgathered}$$