Wave Phenomena

495 Hz or 505 Hz

Step 1: Beat frequency = difference in frequencies of the two sources. Step 2: Beat frequency = 5 Hz (given). Step 3: If one fork has frequency 500 Hz, then the other fork has frequency = 500 ± 5 Hz. Step 4: Therefore, the possible frequencies are 500 + 5 = 505 Hz or 500 - 5 = 495 Hz. Wrong option: 490 and 510 Hz would give 10 beats per second, not 5. Both 495 and 505 are valid since we cannot determine which is higher without additional information.

v/4l

Step 1: In a closed organ pipe, there is a node at the closed end and an antinode at the open end. Step 2: For the fundamental mode (simplest vibration), there is only one quarter-wavelength fitting in the pipe: l = λ/4, so λ = 4l. Step 3: Using v = fλ, fundamental frequency n₁ = v/λ = v/4l. Step 4: For an open pipe, both ends are antinodes, l = λ/2, giving n₁ = v/2l — twice the closed pipe frequency. This is why v/2l is wrong for a closed pipe.

Frequency

Step 1: When an EM wave travels from one medium to another, it interacts with the new medium's atoms/molecules. Step 2: The speed of EM waves changes: v = c/√(μᵣεᵣ), which depends on the medium's properties. Step 3: Since speed changes and v = fλ, the wavelength also changes. Step 4: However, frequency is determined by the source and does NOT change with the medium — the number of oscillations per second remains fixed. This is a fundamental property of wave propagation.

25/9

Step 1: Since I ∝ a², the amplitude ratio a₁/a₂ = √(I₁/I₂) = √(1/16) = 1/4. So a₁ = 1, a₂ = 4. Step 2: Imax ∝ (a₁ + a₂)² = (1 + 4)² = 25. Step 3: Imin ∝ (a₁ - a₂)² = (1 - 4)² = (-3)² = 9. Step 4: Imax/Imin = 25/9. Common mistake: Some students directly use intensity ratio (16/1) without converting to amplitude ratio first, or incorrectly compute (a₁ - a₂)².