A 3.00 m long air column is open at both ends. The frequency of a certain harmonic is 500 Hz and the frequency of the next higher harmonic is 557 Hz. Determine the speed of sound in the air column. The end correction may be neglected.
Question
A 3.00 m long air column is open at both ends. The frequency of a certain harmonic is 500 Hz and the frequency of the next higher harmonic is 557 Hz. Determine the speed of sound in the air column. The end correction may be neglected.
Solution
Sure, let's solve this step by step:
Step 1: Identify the given values.
- Length of the air column (L) = 3.00 m
- Frequency of a certain harmonic (f1) = 500 Hz
- Frequency of the next higher harmonic (f2) = 557 Hz
Step 2: Understand the concept.
- For an air column open at both ends, the harmonics are given by the formula: f = n(v/2L), where n is the harmonic number (an integer), v is the speed of sound, and L is the length of the column.
- The difference between two consecutive harmonics (n and n+1) is Δf = f2 - f1 = v/2L.
Step 3: Substitute the given values into the formula.
- Δf = f2 - f1 = 557 Hz - 500 Hz = 57 Hz
- So, 57 Hz = v/2L
Step 4: Solve for v, the speed of sound.
- v = 2L * Δf = 2 * 3.00 m * 57 Hz = 342 m/s
So, the speed of sound in the air column is 342 m/s.
Similar Questions
By considering your diagrams from part (b) or otherwise, show that the frequency of the nth harmonic of a tube of length L that is open at one end and closed at the other end is given by 𝑓𝑛 = 𝑛 ( 𝑣 4𝐿 ) where v is the speed of sound in air
A 50.0 cm long organ pipe is filled with air and is open at both ends. The speed of sound in air at 0°C is 331 m/s. What is the frequency of the second mode?
If the velocity of sound in air is 340m/s, find a) wavelength when frequency is 256Hzb) frequency when wavelength is 0.85m
A pipe, closed at one end, has a loudspeaker at the open end. For some frequencies of soundfrom the loudspeaker, a stationary sound wave is formed in the air within the pipe with anantinode at the open end of the pipe.0.85 mloudspeaker pipeThe length of the pipe is 0.85 m.The speed of sound in air is 340 m s –1.Which frequency of sound from the loudspeaker would not produce a stationary wave?A 100 Hz B 200 Hz C 300 Hz D 500 Hz
A resonance occurs with a tuning fork and air column of size 12cm. the next higher resonance occurs with an air column of 38cm. What is the frequency of the tuning fork? Assume that the speed of sound is 312m/s
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.