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Published byUrsula Hart Modified over 5 years ago

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**Principle of Superposition Interference Stationary Waves**

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**What happens when two waves occupy the same space at the same time?**

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**Principle of Superposition**

When two waves occupy the same space at the same time, their displacements add up (algebraically.) Interference

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**Constructive Interference**

Amplitudes increase

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**Destructive Interference**

Amplitudes decrease Sometimes, they completely cancel each other out

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**Interference and Path Difference**

Consider two sources of waves at a distance from each other. What conditions are necessary for complete destructive interference to occur at a point?

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**What conditions are necessary for complete destructive interference to occur at a point?**

The same intensity or amplitude The same type of wave They have the same frequency or period

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**Their path difference must be N (λ/2) Where N = 1, 3,5,….**

What conditions are necessary for complete destructive interference to occur at a point? They must be in phase Their path difference must be N (λ/2) Where N = 1, 3,5,….

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**Their path difference must be N (λ) Where N = 1, 2,3,….**

What should be their path difference for constructive interference to occur at a point? Their path difference must be N (λ) Where N = 1, 2,3,….

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Example 1 Two loudspeakers A and B emit are driven by the same amplifier and emit in phase waves.

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Example 1 For what frequencies does constructive interference occur at P?

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Example 1 For what frequencies does destructive interference occur at P?

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Example 2 Two identical sources of sound are situated 80 cm apart as shown. They always vibrate in phase with each other.

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Example 2 A microphone is placed 100 cm from S1 as shown. The speed of sound is 330 ms-1. How many frequencies between 1.0 kHz to 4.0 kHz will produce no sound at M?

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**Standing Waves (a.k.a. Stationary Waves)**

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**Formation of Standing Waves**

Incident waves travel in one direction and are reflected back Incident and reflected waves interfere Points that constructively interfere form antinodes Points that destructively interfere form nodes

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**Standing Waves (Which is a standing wave?)**

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**Do standing waves have wave speed?**

Yes Wave speed is the speed of the incident and reflected waves.

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**Equations for Standing Waves**

Fixed Ends String Instruments ƒ = n (v/2L) Where n = 1,2,3,…

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**Equations for Standing Waves**

One fixed end, One open end Percussion instruments Water pipe ƒ = n (v/4L) Where n = 1,3,5,…

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**Equations for Standing Waves**

Two Open ends Some wind instruments ƒ = n (v/2L) Where n = 1,2,3,… Similar to two fixed ends

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Example 1 One of the 63.5-cm long strings of a guitar is tuned to produce the note B3 (frequency 245 Hz) when vibrating in its fundamental mode. Find the speed of the transverse waves on the string.

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Example 1 If the speed of sound in the air is 344 ms-1, find the frequency and wavelength of the sound wave produced in the air by the vibrating string.

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**Example 2 (A Tale of Two Pipes)**

One day when the speed of sound is 345 ms-1, the fundamental frequency of a stopped organ pipe is 220 Hz. How long was this pipe?

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**Example 2 (A Tale of Two Pipes)**

The second overtone of this pipe has the same wavelength as the third harmonic of an open pipe. How long is the open pipe?

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