A metre-long tube open at one end, with a movable piston at the other end, shows resonance with a fixed frequency source (a turning fork of frequency 340 Hz) when the tube length is 25.5 cm or 79.3 cm. Estimate the speed of sound in air at the temperature of the experiment. The edge effect may be neglected.

Certainly! Let's break down the problem step by step.

Firstly, we need to understand the concept of resonance. In this scenario, the tube resonates with a fixed frequency source, which is a tuning fork with a frequency of 340 Hz. The resonance occurs when the length of the tube is such that it allows for a standing wave to form, with nodes at both ends and an antinode in the middle.

Given that the tube length for resonance is observed at 25.5 cm and 79.3 cm, we can use the formula for the fundamental frequency of a closed-open pipe to find the speed of sound.

The formula for the fundamental frequency of a closed-open pipe is:

f=v2Lf=2Lv

Where:

• ff is the frequency of the sound wave (340 Hz in this case, given by the tuning fork).
• vv is the speed of sound in air.
• LL is the length of the tube.

We have two sets of data for LL, which gives us two equations:

f1=v2L1f1=2L1v f2=v2L2f2=2L2v

We can rearrange these equations to solve for vv:

v=2f1L1v=2f1L1 v=2f2L2v=2f2L2

Now, we can average the values of vv obtained from these two equations to get a more accurate estimation of the speed of sound.

vavg=(2f1L1+2f2L2)2vavg=2(2f1L1+2f2L2)

Plugging in the values:

vavg=(2×340 Hz×0.255 m+2×340 Hz×0.793 m)2vavg=2(2×340Hz×0.255m+2×340Hz×0.793m)

vavg=(340×0.255+340×0.793)2vavg=2(340×0.255+340×0.793)

vavg=(86.7+269.62)2vavg=2(86.7+269.62)

vavg=356.322vavg=2356.32

vavg=178.16 m/svavg=178.16m/s

So, the estimated speed of sound in air at the temperature of the experiment is approximately 178.16 m/s178.16m/s.

In real-life scenarios, this value might deviate slightly due to factors like temperature and humidity affecting the speed of sound, but this calculation provides a good approximation based on the given data.