A 1289 Hz sound from the speaker enters a tube at point A.
It then takes two paths, ACD or ABD. Minimum sound is heard when ACD has a length of 94.2 cm and ABD has a length of 41.0 cm. The length of ACD is slowly increased until the point of maximum loudness is found when ACD is 108 cm (ABD is left unchanged). What is the speed of sound?
The answer for the speed of sound is 343 m/s but i have no idea how to get it. i keep getting 355 m/s
To find the speed of sound in this scenario, we can use the concept of resonance. Resonance occurs when the length of a tube is such that a sound wave traveling through it reflects back and reinforces itself, resulting in maximum loudness.
First, let's identify the fundamental frequency or first harmonic of the tube, which is the frequency at which resonance occurs. In this case, the frequency of the sound is given as 1289 Hz.
The fundamental frequency of a tube is related to its length by the formula:
f = (v / (2L))
where f is the frequency, v is the speed of sound, and L is the length of the tube.
In the scenario where maximum loudness is achieved, the length of ACD is 108 cm. Assuming ABD remains unchanged at 41.0 cm, the total length of the tube is 108 cm + 41.0 cm = 149 cm.
Using the given frequency and the total length of the tube, we can rearrange the formula to solve for the speed of sound (v):
v = 2Lf
Plugging in the values:
v = 2 * 149 cm * 1289 Hz
Now, we need to make sure all the units are consistent. Let's convert centimeters to meters:
v = 2 * 1.49 m * 1289 Hz
= 3.78 m * 1289 Hz
Lastly, we multiply the two numbers to get the speed of sound:
v ≈ 4878 m/s
Therefore, the speed of sound in this scenario is approximately 4878 m/s.
However, if you are getting a value of 355 m/s, it seems like there may have been an error in your calculations. Make sure you double-check your unit conversions and the values used in the calculations.