Question

How long will sound take to travel in:
(A) Iron ring?
(B) Air?
Both $3.3km$ in length, take speed of sound in air to be $330m/s$ and in iron to be $5280m/s$

Answer 1

To solve this question, we need to use the basic formula of the speed. Using the values of the length and the speed in different mediums, we can get the required values of time.
Formula used: The formula used to solve this question is given by
$\Rightarrow v = \dfrac{d}{t}$ , here $v$ is the speed, $d$ is the distance covered, and $t$ is the time elapsed.

Complete step by step solution:
As the length to be covered in both the cases is equal to $3.3km$, so the distance to be covered by the sound in both the cases is
$\Rightarrow d = 3.3km$
$\Rightarrow d = 3.3 \times 1000m = 3300m$ …………………….(i)
(a) For iron ring
Let the time required in this case be ${t_1}$
According to the question, the speed of sound in the iron is equal to $5280m/s$. That is, in this case $v = 5280m/s$ ……………………...(ii)
We know that the speed is given by
$\Rightarrow v = \dfrac{d}{t}$
So for this case
$\Rightarrow v = \dfrac{d}{{{t_1}}}$
From (i) and (ii)
$\Rightarrow 5280 = \dfrac{{3300}}{{{t_1}}}$
$\Rightarrow {t_1} = \dfrac{{3300}}{{5280}}$
On solving, we get
$\Rightarrow {t_1} = 0.625s$
Hence, the time required by sound to travel through the iron ring is equal to $0.625s$
(b) For air
Let the time required in this case be ${t_2}$
According to the question, the speed of sound in the air is equal to $330m/s$. That is, in this case $v = 330m/s$ ………………………..(iii)
We know that the speed is given by
$\Rightarrow v = \dfrac{d}{t}$
So in this case
$\Rightarrow v = \dfrac{d}{{{t_2}}}$
Putting (i) and (iii), we get
$\Rightarrow 330 = \dfrac{{3300}}{{{t_2}}}$
$\Rightarrow {t_2} = \dfrac{{3300}}{{330}}$
On solving, we get
$\Rightarrow {t_2} = 10s$

Hence, the time required by sound to travel through the air is equal to $0.625s$

Note:
Do not forget to convert the units of all the given quantities in their respective SI units. In these types of entirely numerical based questions, the units are intentionally given in different units. Like in this problem, the length was given in kilometres, which is not an SI unit. It was supposed to be converted to meters. If you forget to convert, the final answer will be incorrect.