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3 years ago

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The opening to a cave is a tall, 30.0-cm-wide crack. A bat is preparing to leave the cave emits a 30.0 kHz ultrasonic chirp. How

wide is the "sound beam" 100. M outside the cave opening? Use v sound= 340. M/s.

1 answer:

Vlada [557]3 years ago

4 0

Answer:

The value is $w = 7.54 \ m$

Explanation:

From the question we are told that

The length of the crack is $a = 0.3 \ m$

The frequency is $f = 30.0 \ kHz = 30 *10^{3} \ Hz$

The distance outside the cave that is being consider is $D = 100 \ m$

The speed of sound is $v_s = 340 \ m/s$

Generally the wavelength of the wave is mathematically represented as

$\lambda = \frac{v}f}$

=> $\lambda = \frac{340 }{30*10^{3}}$

=> $\lambda = 0.0113 \ m/s$

Generally for a single slit the path difference between the interference patterns of the sound wave and the center is mathematically represented as

$y = \frac{ n * \lambda * D}{a}$

=> $y = \frac{ 1 * 0.0113 * 100}{0.3}$

=> $y = 3.77 \ m$

Generally the width of the sound beam is mathematically represented as

$w = 2 * y$

=> $w = 2 * 3.77$

=> $w = 7.54 \ m$

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For light of wavelength 589 nm, calculate the critical angles for the following substances when surrounded by air.

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(1) The critical angles for the fused quartz is 44⁰,

(2) The critical angles for the polystyrene is 39⁰.

(3) The critical angles for the sodium chloride is 41⁰.

<h3>What is Critical angles?</h3>

In optics, the critical angle is the topmost angle at which a shaft of light traveling in one transparent medium can strike the boundary between that medium and another with a lower refractive indicator without being fully reflected within the first

Critical angles for the different medium.

θ $=sin^{-1}\frac{n_{2} }{n_{1} }$

where;

$n_{2}$ is the refractive index of air = 1

$n_{1}$ is the refractive index of the given substances.

Refractive index of quartz glass = 1.46

Refractive index of polystyrene = 1.59

Refractive index of sodium chloride = 1.54

Critical angles for quartz glass:

$\theta_{\text {crit }}=\sin ^{-1} \frac{1.00029}{1.46}\\$

$\theta_{\text {crit }}=44^{o}$

Critical angles for polystyrene

$$\theta_{\text {crit }}=\sin ^{-1} \frac{1.00029}{1.59}\\\\$

$\theta_{\text {crit }}=39^{\circ}$

Critical angles for Sodium Chloride

$$\theta_{\text {crit }}=\sin ^{-1} \frac{1.00029}{1.54}\\$

$\theta_{\text {crit }}=41^{o}$

Thus, the critical angles for the quartz glass is 44⁰, the critical angles for the polystyrene is 39 ⁰ and the critical angles for the sodium chloride is 41⁰.

To know more about critical angle visit:
brainly.com/question/3314727

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I understand that the question you are looking for is:

"For light of wavelength 589 nm, calculate the critical angles for the following substances when surrounded by air.

(a) Fused Quartz

(b) Polystyrene

(c) Sodium chloride"

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2 years ago

An electron enters a region of space containing a uniform 2.71 × 10 − 5 2.71×10−5 T magnetic field. Its speed is 197 197 m/s and

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Answer:

r = 0.0414mm

F = 757,692.3Hertz

Explanation:

If the body enters space with uniform magnetic field B, the force experienced by the object is expressed as

F = qvBsintheta... 1

Also, if the body undergoes a circular motion, the force experienced by the body in a circular path is given as

Fc = mv²/r... 2

Equating both forces

F = Fc

qvBsin theta = mv²/r

Since the body enters perpendicular to the field, theta = 90°

The equality becomes;

qvB sin90° = mv²/r

qvB = mv²/r

qB = mv/r

r = mv/qB

Given mass of the electron m = 9.11×10^-31kg

Velocity of the object v = 197m/s

Charge on the electron q = 1.6×10^-19C

Magnetic field B = 2.71×10^-5T

Substituting this value into the equation to get the radius r we have;

r = 9.11×10^-31 × 197/1.6×10^-19 × 2.71×10^-5

r = 1794.67×19^-31/4.336×10^-24

r = 413.89×10^-7

r = 0.0000414m

r = 0.0414mm

b) Frequency of the motion F = w/2π where w is the angular velocity

Since w = v/r

F = (v/r)/2π

F = v/2πr

F = 197/2π(0.0000414)

F = 757,692.3Hertz

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