NCERT Solutions for Class 9 Science Chapter 11 Sound
Page No. 138 Exercise Question 7.
9th Science Chapter 11 Sound NCERT Academic Session 2023-2024
CBSE Board and Others state Board
Description:
Sound waves in air result from vibrations, forming compressions and rarefactions that propagate energy. They require a medium, like air, to travel, moving particles in cycles. Characteristics include frequency (pitch) and amplitude (volume). Our ears detect these vibrations, converting them into the sound we perceive.
The speed of sound in a medium depends on the properties of that medium. In general, sound travels faster in denser materials.
Let’s denote:
v_air as the speed of sound in air.
v_aluminium as the speed of sound in aluminium.
The ratio of the times taken by the sound wave in air and aluminium to reach the second child can be found using the formula:
Ratio of times = (Distance)/(Speed)
Since the two children are at opposite ends of the aluminium rod, the sound wave must travel through both air and the aluminium rod to reach the second child.
Let’s denote:
L as the length of the aluminium rod.
The total distance the sound wave travels to reach the second child is L (through the aluminium rod).
The time taken by the sound wave in air is:
Time taken in air = (Distance in air)/(Speed in air) = (L)/{v_air)
The time taken by the sound wave in aluminium is:
Time taken in aluminium = (Distance in aluminium)/(Speed in aluminium) = (L)/(v_aluminium)
Therefore, the ratio of times taken by the sound wave in air and in aluminium to reach the second child is:
Ratio = (Time taken in air)/(Time taken in aluminium) = ((L)/(v_air))/((L)/(v_aluminium) = (v_aluminium)/(v_air)
This ratio is equal to the ratio of the speeds of sound in aluminium and air.
If you have the values for the speeds of sound in air (v_air) and in aluminium (v_aluminium), you can directly calculate this ratio. Typically, the speed of sound in aluminium is much higher than in air, so the ratio would be greater than 1.