Answer :
The frequency of the sound produced by the pan flute is 556.7 Hz.
As the temperature drops, the frequency of the pan flute's sound also drops. This is due to the fact that when temperature drops, so does the sound speed in air.
1. Frequency calculation given the period
T = 2.3 msec, first
We are aware that frequency is the inverse of period. Therefore,
f=1/T, f=1/0.0023, and f=434.78 Hz
The sound has a 434.78 Hz frequency.
b. T = 0.005 sec
By applying the formula,
f=1/T, f=1/0.005, and f=200 Hz
The sound has a frequency of 200 Hz.
c. T = 25 µsec
It is stated in microseconds. Before computing the frequency, we must convert it to seconds.
T = 25 × 10⁻⁶ sec
By applying the formula,
f = 1/T
f = 1/(25 × 10⁻⁶)
f = 40,000 Hz
The sound has a frequency of 40,000 Hz.
2. Period calculation given frequency:
a. f = 660 Hz
By applying the formula,
T = 1/f
T = 1/660
T = 0.001515 sec
The The sound has a 0.001515 second period.
b. f = 100.5 MHz
The frequency is expressed in MHz. Prior to computing the period, we must convert it to Hz.
f = 100.5 × 10⁶ Hz
By applying the formula,
T = 1/f
T = 1/(100.5 × 10⁶)
T = 9.9256 × 10⁻⁹ sec
The sound has a duration of 9.9256 109 seconds.
c. f = 2.5 KHz
The frequency is expressed in KHz. Prior to computing the period, we must convert it to Hz.
f = 2.5 × 10³ Hz
By applying the formula,
T = 1/f
T = 1/(2.5 × 10³)
T = 0.0004 sec
The sound has a 0.0004 second period.
3. A pan flute's frequency may be calculated using the following information: the pipe is 15 cm long and closed on one end. The formula may be used to determine the sound's frequency.
f = (n × v)/(4L)
where L is the length of the pipe, v is the speed of sound in air, and n is the harmonic number (1, 2, 3,...).
When air is heated to 450 degrees Celsius, the speed of sound in the air changes. We may approximate using
v = 331 + 0.6T
where T is the Celsius temperature.
v = 331 + 0.6 × 45 v = 358.4 m/s
L = 15 cm = 0.15 m
When n = 1, the fundamental frequency,
f = (n × v)/(4L)
f = (1 × 358.4)/(4 × 0.15) f = 597.3 Hz
The pan flute produces sound at a frequency of 597.3 Hz.
v = 331 if the pipe is blasted at 50 degrees Celsius. + 0.6 × 5 v = 334 m/s
L = 15 cm = 0.15 m
When n = 1, the fundamental frequency,
f = (n × v)/(4L)
f = (1 × 334)/(4 × 0.15)
f = 556.7 Hz
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