Skip to content
Login Register

#steel rod

11 public questions tagged with this topic.

Sound Waves, Reflection and Characteristics

A steel rod of length 2 m has a fundamental frequency of longitudinal vibrations of 1.25 kHz. What is the speed of sound

**Longitudinal vibrations in rods** clamped at middle have fundamental with node at clamp and antinodes at ends, f₁ = v/(2L), v speed of sound in material (m/s). This relation allows v extraction from measured f₁ and length L, e.g., v = 2L·f₁. For rod clamped at middle, fundamental: v₁ = (v/2L) . 1250 = (v/2 × 2) ⇒ v = 1250 × 4 = 5000 m/s . Using v = fλ and standing-wave condition fₙ = n v/(2L) or v/(4L) as applicable, calculation yields 5000 m/s, illustrating frequency-length-speed interdependence and quantization by boundaries.

Ref: NCERT > Physics Book > Waves > Sound Waves, Reflection and Characteristics

View Details
Sound Waves, Reflection and Characteristics

A steel rod of length 1.5 m has a fundamental frequency of longitudinal vibrations of 2 kHz. What is the speed of sound

**Longitudinal vibrations in rods** clamped at middle have fundamental with node at clamp and antinodes at ends, f₁ = v/(2L), v speed of sound in material (m/s). This relation allows v extraction from measured f₁ and length L, e.g., v = 2L·f₁. For rod clamped at middle, fundamental: v₁ = (v/2L) . 2000 = (v/2 × 1.5) ⇒ v = 2000 × 3 = 6000 m/s . Using v = fλ and standing-wave condition fₙ = n v/(2L) or v/(4L) as applicable, calculation yields 6000 m/s, illustrating frequency-length-speed interdependence and quantization by boundaries.

Ref: NCERT > Physics Book > Waves > Sound Waves, Reflection and Characteristics

View Details
Wave Equation and Displacement Relation

A steel rod of length 2 m and density 7800 kg/m³ has a longitudinal wave speed of 5000 m/s. What is its Young’s modulus?

**Displacement relation** encodes λ = 2π/k and f = ω/2π. Comparing given equation y = a sin(kx - ωt) with standard form yields k and ω, hence λ = 2π/k and v = ω/k, essential for identifying propagation characteristics and phase. Speed: v = √((Y/rho)) . 5000 = √((Y/7800)) ⇒ 5000² = (Y/7800) . Y = 5000² × 7800 = 1.95 × 10¹¹ Pa . Using v = fλ and standing-wave condition fₙ = n v/(2L) or v/(4L) as applicable, calculation yields 1.95 × 10¹¹ Pa, illustrating frequency-length-speed interdependence and quantization by boundaries.

Ref: NCERT > Physics Book > Waves > Wave Equation and Displacement Relation

View Details
Sound Waves, Reflection and Characteristics

A steel rod of density 7800 kg/m³ has a Young’s modulus of 2 × 10¹¹ Pa. What is the speed of a longitudinal wave in the

**Sound wave reflection** at rigid wall behaves like string fixed end, displacement inverted. Equation of reflected wave includes sign change and direction reversal, amplitude unchanged but sign may flip, explaining standing wave formation with incident wave. Speed: v = √((Y/rho)) = √((2 × 10¹¹/7800)) ≈ √(2.56 × 10⁷) ≈ 5060 m/s . Using v = fλ and standing-wave condition fₙ = n v/(2L) or v/(4L) as applicable, calculation yields 5060 m/s, illustrating frequency-length-speed interdependence and quantization by boundaries.

Ref: NCERT > Physics Book > Waves > Sound Waves, Reflection and Characteristics

View Details
Sound Waves, Reflection and Characteristics

A steel rod of length 1.8 m has a fundamental frequency of longitudinal vibrations of 1.5 kHz. What is the speed of soun

**Longitudinal vibrations in rods** clamped at middle have fundamental with node at clamp and antinodes at ends, f₁ = v/(2L), v speed of sound in material (m/s). This relation allows v extraction from measured f₁ and length L, e.g., v = 2L·f₁. For rod clamped at middle, fundamental: v₁ = (v/2L) . 1500 = (v/2 × 1.8) ⇒ v = 1500 × 3.6 = 5400 m/s . Using v = fλ and standing-wave condition fₙ = n v/(2L) or v/(4L) as applicable, calculation yields 5400 m/s, illustrating frequency-length-speed interdependence and quantization by boundaries.

Ref: NCERT > Physics Book > Waves > Sound Waves, Reflection and Characteristics

View Details
Sound Waves, Reflection and Characteristics

A steel rod of length 1.2 m has a fundamental frequency of longitudinal vibrations of 2.5 kHz. What is the speed of soun

**Sound wave reflection** at rigid wall behaves like string fixed end, displacement inverted. Equation of reflected wave includes sign change and direction reversal, amplitude unchanged but sign may flip, explaining standing wave formation with incident wave. For rod clamped at middle, fundamental: v₁ = (v/2L) . 2500 = (v/2 × 1.2) ⇒ v = 2500 × 2.4 = 6000 m/s . Using v = fλ and standing-wave condition fₙ = n v/(2L) or v/(4L) as applicable, calculation yields 6000 m/s, illustrating frequency-length-speed interdependence and quantization by boundaries.

Ref: NCERT > Physics Book > Waves > Sound Waves, Reflection and Characteristics

View Details
Bulk Modulus and Compressibility

A steel rod of radius 0.01m and length 1.5m is subjected to a tensile force producing a stress of 4×107N/m2. What is the

Stress: Stress = FA. Area: A = πr2 = 3.14×(0.01)2 = 3.14×10−4m2. Force: F = Stress×A = 4×107×3.14×10−4 = 1.256×104N. As per NCERT, applying relevant law/formula with correct units and sign convention leads to 1.256×104N. This satisfies dimensional consistency and physical conditions given, so option A is scientifically correct.

Ref: University Physics, Chapter 17: Thermal Expansion.

View Details