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#standing waves

3 public questions tagged with this topic.

Doppler Effect

Why are standing waves formed in musical instruments like a guitar?

**Relative motion** changes effective wavelength encountered. For moving source approaching stationary observer, wavelength ahead λ' = (v - v_s)/f, so f' = v/λ' = f·v/(v - v_s) > f, basis for calculating apparent pitch shift in sound. Standing waves in a guitar arise from the interference of waves reflected at fixed ends (e.g., bridge and nut), producing discrete frequencies (harmonics) determined by string length. Using v = fλ and standing-wave condition fₙ = n v/(2L) or v/(4L) as applicable, calculation yields Due to reflection at boundaries, illustrating frequency-length-speed interdependence and quantization by boundaries.

Ref: NCERT > Physics Book > Waves > Doppler Effect

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Superposition and Interference of Waves

Which factor directly governs the formation of nodes and antinodes in a standing wave?

**Wave addition** governed by phase difference determines resultant intensity ∝ A². Phase arises from path difference Δ = (2π/λ)·Δx, and resultant formula captures interference condition quantitatively for NCERT problems. The boundary conditions (e.g., fixed or free ends) determine where nodes (zero displacement) and antinodes (maximum displacement) occur by enforcing specific wave patterns. Using v = fλ and standing-wave condition fₙ = n v/(2L) or v/(4L) as applicable, calculation yields Boundary conditions, illustrating frequency-length-speed interdependence and quantization by boundaries.

Ref: NCERT > Physics Book > Waves > Superposition and Interference of Waves

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Stationary Waves and Standing Waves in Strings

A string of length 2 m fixed at both ends has a wave speed of 60 m/s. What is the frequency of its third harmonic?

**Stationary waves** form when identical progressive waves traveling opposite directions interfere, y = 2A sin(kx) cos(ωt), nodes where sin(kx)=0, antinodes where |sin(kx)|=1. For string fixed at both ends, allowed wavelengths λₙ = 2L/n, frequencies fₙ = n·v/(2L), n = 1,2,3… harmonic number. v_n = (n v/2L) . Third harmonic ( n = 3 ): v₃ = (3 × 60/2 × 2) = (180/4) = 45 Hz . Using v = fλ and standing-wave condition fₙ = n v/(2L) or v/(4L) as applicable, calculation yields 45 Hz, illustrating frequency-length-speed interdependence and quantization by boundaries.

Ref: NCERT > Physics Book > Waves > Stationary Waves and Standing Waves in Strings

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