Respuesta :
Answer:
water heights of the tube are 0.851 m , 0.553 m, 0.255 m
Explanation:
given data
frequency = 580 Hz
temperature = 20°C
tube = 1 m
to find out
water heights of the tube
solution
we will apply here formula for length that is
length L = v ( 2n -1 ) / 4f
here v is velocity o sound that is 343.2 m/s
so for n = 1
L = 343.2 ( 2(1) -1 ) / 4(580) = 0.147931 m
for n = 2
L = 343.2 ( 2(2) -1 ) / 4(580) = 0.443793 m
for n = 3
L = 343.2 ( 2(3) -1 ) / 4(580) = 0.739655 m
for n = 4
L = 343.2 ( 2(4) -1 ) / 4(580) = 1.035517 m is greater than 1
and so here height is measured less than 1 m
so water heights of the tube are 1 m - 0.147931 m , 1 m - 0.443793 m, 1 m - 0.739655 m
so water heights of the tube are 0.851 m , 0.553 m, 0.255 m
Wavelength is the distance between two points of the two consecutive waves.
The water heights, measured from the bottom of the tube is 0.1422 m, 0.285 m, 0.427, 0.569 m and so
What is the wavelength of the wave?
Wavelength is the distance between two points of the two consecutive waves. It can be given as,
[tex]\lambda=\dfrac{v}{f}[/tex]
Here [tex]v[/tex] is the speed of sound (330 m/s) and f is the frequency.
Given information-
The length of the vertical tube is 1.0 m long.
The temperature of water fill in the tube is 20 degree Celsius.
The frequency of the vibrating fork is 580 Hz.
Put the value in the above equation to find the wavelength as,
[tex]\lambda=\dfrac{330}{580} \\\lambda=0.569 \rm m \\[/tex]
As the resonance condition in tube occurs. Thus the length of the tube can be find out as,
[tex]L=\dfrac{n\lambda}{4}[/tex]
Here,
[tex]n=1,2,3,4.....[/tex] so on.
Put the values as,
[tex]L_1=\dfrac{1\times0.569}{4}=0.14224\\L_2=\dfrac{2\times0.569}{4}=0.2845\\L_3=\dfrac{3\times0.569}{4}=0.0.4267\\L_3=\dfrac{4\times0.569}{4}=0.0.569\\[/tex]
So on...
Thus the water heights, measured from the bottom of the tube is 0.1422 m, 0.285 m, 0.427, 0.569 m and son on.
Learn more about the wavelength here;
https://brainly.com/question/10728818
