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Archy [21]
3 years ago
15

Organ pipe a, with both ends open, has a fundamental frequency of 340 hz. the third harmonic of organ pipe b, with one end open,

has the same frequency as the second harmonic of pipe
a. how long are (a) pipe a and (b) pipe b? (take the speed of sound to be 343 m/s.)
Physics
1 answer:
Sphinxa [80]3 years ago
7 0
The fundamental frequency of the open pipe A
Length 'L₀' is, f₀ = U/2L₀ = 340 H₂
the speed of sound in air V=  343m/s
∴343/2L₀ = 340 → length L₀ = 343/2 ×340 = 0.5044 = 50.44
The third harmonic of closed pipe 'B' is 
F3₀ = 3V/4LC
The second harmonic of open pipe 'A'  is
f2₀ = 2V/2L₀
∴ 3V/4LC = 2V/2L →L₀ = 3L₀/4
⇒ The length of closed pipe B is 
Lc = 37.83cm

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A ballast is dropped from a stationary hot-air balloon that is at an altitude of 576 ft. Find (a) an expression for the altitude
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Answer:

<h2>a) S = \frac{1}{2}gt^2\\</h2><h2>b) 6secs</h2><h2>c) 192ft</h2>

Explanation:

If a ball dropped from a stationary hot-air balloon that is at an altitude of 576 ft, an expression for the altitude of the ballast after t seconds can be expressed using the equation of motion;

S = ut + \frac{1}{2}at^{2}

S is the altitude of the ballest

u is the initial velocity

a is the acceleration of the body

t is the time taken to strike the ground

Since the body is dropped from a stationary air balloon, the initial velocity u will be zero i.e u = 0m/s

Also, since the ballast is dropped from a stationary hot-air balloon, the body is under the influence of gravity, the acceleration will become acceleration due to gravity i.e a = +g

Substituting this values into the equation of the motion;

S = 0 + \frac{1}{2}gt^2\\ S = \frac{1}{2}gt^2\\

a) An expression for the altitude of the ballast after t seconds is therefore

S = \frac{1}{2}gt^2\\

b) Given S = 576ft and g = 32ft/s², substituting this into the formula in (a);

576 = \frac{1}{2}(32)t^2\\\\\\576*2 = 32t^2\\1152 = 32t^2\\t^2 = \frac{1152}{32} \\t^2 = 36\\t = \sqrt{36}\\ t = 6.0secs

This means that the ballast strikes the ground after 6secs

c) To get the velocity when it strikes the ground, we will use the equation of motion v = u + gt.

v = 0 + 32(6)

v = 192ft

7 0
4 years ago
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