Humans can hear sounds with frequencies up to about 20.0 kHz, but dogs can hear frequencies up to about 40.0 kHz. Dog whistles are made to emit sounds that dogs can hear but humans cannot. If the part of a dog whistle that actually produces the high frequency is made of a tube open at both ends, what is the longest possible length for the tube? (Assume a temperature of 20° C.)
mm
I used this formula L = v/2*f1, I end up with 0.43 cm which should be 4.3mm but its wrong and I don't know why. Could someone please explain it to me. Thank you!
length is half wavelength.
frequency*2Length=velocity sound
length= (331+.6*20)/2*40E3
= 343/80E3=4.3mm
Thanks.Thats what I got too as my answer, but for some reason its wrong :/ I have no clue why.
To determine the longest possible length for the tube of a dog whistle that emits sounds at frequencies dogs can hear but humans cannot, you can use the formula:
L = v / (2 * f1)
Where:
L = Length of the tube
v = Speed of sound in air
f1 = Frequency of the sound
In this case, the highest frequency that dogs can hear is 40.0 kHz, which is 40,000 Hz.
First, you need to convert the frequency from kilohertz (kHz) to hertz (Hz) by multiplying it by 1000.
40.0 kHz * 1000 = 40,000 Hz
Next, you need to determine the speed of sound in air at a temperature of 20°C. The equation for the speed of sound in air is given by:
v = 331.4 + 0.6 * T
Where:
v = Speed of sound in m/s
T = Temperature in degrees Celsius
Plugging in the temperature of 20°C into the equation, you get:
v = 331.4 + 0.6 * 20
v = 331.4 + 12
v = 343.4 m/s
Now you can substitute the values into the formula:
L = 343.4 / (2 * 40,000)
Calculating this division, you get:
L = 343.4 / 80,000
L = 0.0042925 m
To convert this to millimeters, you multiply the length by 1000:
L = 0.0042925 m * 1000
L ≈ 4.29 mm
Therefore, the longest possible length for the tube of the dog whistle is approximately 4.29 mm.