Question

Table shows the speed of sound in a few media at atmospheric pressure.

State	Substance/Medium	Approximate speed
Solid	Steel	\(5000 \mathrm{~m} \mathrm{~s}^{-1}\)
Liquid	Water	\(1500 \mathrm{~m} \mathrm{~s}^{-1}\)
Gas	Air	\(340 \mathrm{~m} \mathrm{~s}^{-1}\)

Compare the speeds in different media by finding the ratio of

1. the speed of sound in water with respect to the speed in the air. 
2. the speed of sound in steel with respect to the speed in the water.

Answer 1

Given:

Speed of sound in air, \(v_a = 340 \text{ m/s}\)

Speed of sound in water, \(v_w = 1500 \text{ m/s}\)

Speed of sound in steel, \(v_s = 5000 \text{ m/s}\)

(i) Find the ratio of the speed of sound in water to that in air.

Formula:

\[ \text{Ratio}=\frac{v_w}{v_a} \]

Substituting the values,

\[ =\frac{1500}{340} \]

\[ =\frac{75}{17} \]

\[ \approx 4.41 \]

The ratio of speeds in water and air is 75 : 17 (approximately 4.41 : 1).

(ii) Find the ratio of the speed of sound in steel to that in water.

Formula:

\[ \text{Ratio}=\frac{v_s}{v_w} \]

Substituting the values,

\[ =\frac{5000}{1500} \]

\[ =\frac{10}{3} \]

\[ \approx 3.33 \]

The ratio of speeds in steel and water is 10 : 3 (approximately 3.33 : 1).