Two stereo speakers mounted 4.52 m apart on a wall emit identical sound waves. Y

Question

Two stereo speakers mounted 4.52 m apart on a wall emit identical sound waves. You are standing at the opposite wall of the room at a point directly between the two speakers. You walk 2.11 m parallel to the wall, to a location where you first notice that the sound intensity is much less. If the wall along which you are walking is 10.7 m from the wall with the speakers, what is the wavelength of the sound waves? 1.71 m 2.05 m 2.57 m 2.91 m A 350-g air track cart on a horizontal air track is attached to a string that goes over a pulley with a moment of inertia of 6.00 times 10-6 kg m2 and a radius of 1.35 cm. The string is pulled vertically downward by a force of 2.50 N. What is the tension in the string between the pulley and the cart? 4.58 N 2.50 N 1.85 N 2.29 N

Explanation / Answer

24)

Given:

distance between speaker-1 and speaker-2 = 4.52
distance between the two wall = 12.5
while the person walking parallel to the speaker wall, he created a difference distance that means path difference (pd)

Solution:

Conditions for the constructive interference = Path difference = (0+n)Lambda

Condition for the destructive interference = Path difference = [(1/2)+n ]Lambda

So, for the destructive interference (since the intensity is much less)
pd = (n + 0.5)(lambda), where n=0, 1, 2, 3, etc, Here n is an integer
pd = (0 + 0.5)(lambda)

Here lambda represents the wavelength of the sound waves

there are two right triangles

triangle-1
side = 10.7 m
side = 4.52/2 + 2.11 = 4.37 3
d1 = sqrt(10.7^2 + 4.37^2) = 11.558 m

triangle-2
side = 10.7 m
side = 4.52/2 - 2.11 = 0.15 m
d2 = sqrt(10.7^2 + 0.15^2) = 10.7 m

pd = d1 - d2 = 11.5 m - 10.7 m
= 0.858 m
(it does not matter whether d1 is greater or smaller than d2)
pd = (0.5*lambda)

Therefore

Lambda = pd / 0.5
= 0.858 m / 0.5
= 1.716 m
So option A is the answer

25)

Given:

Mass of the tract cart m = 350 g
= 0.350 Kg
Radius of the pulley r = 1.35 cm
= 0.0135 m
Applied force = 2.5 N

Force balance on the cart:

T = m*a
T - m*a = 0
This is equation no.1
(a is the acceleration of the cart)

Force balance on the pulley
(F - T)*r - ?*I = 0
This is equation no.2
r = pulley radius
F the applied force
? the angular acceleration of the pulley I its moment of inertia
T - Tension between the pulley and the cart

However, ? = a/r
where
a = tangential acceleration of the pulley,
which must be the same as the acceleration of the cart and string. The second equation becomes

(F - T)*r - (a/r)*I = 0
This is equation no.3

Moment of inertis = I = m*r^2

solve for a, from the third equation

a = (F - T)*r

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